Targeted consequences? Probably not specifically. Generally, it's a good idea for any government to keep the people who grow its food alive, and China was no different. There were some exceptions, like the Manchu 'Queue Order' which was aimed at all adult Han males and forced them to comply with the Manchu hairstyle and code of dress (the long ponytail thing). These kinds of orders did pop up through history, and were often brutally enforced. But as collateral, yeah there was a good chance you'd probably die. Rebellions in China and dynastic upheavals were never... pretty. Let's say for instance that your LARPing character is living during the An Lushan rebellion. The high estimate of deaths during this rebellion at the height of Tang power is two-thirds of the Empire's population dying. So I'd reckon you had a large chance of dying in that kind of a situation. Actual dynastic transitions varied. Conquest dynasties were generally much more brutal. The conquest of the Song by the mongols saw millions die in the carnage and the conquest of the Ming by the Qing killed tens of millions as well. Specifically in the case of the Mongols, you also had a good chance of dying during the actual dynasty's rule as well as the Mongol dynasty was not particularly well maintained. You can read this account of a member of the gentry commentating on Mongol rule of China right around the era of the Red Turban rebellions.
As far as conscription goes, conscription was already commonplace to begin with. Corvee labor was often used by the government to conscript peasants and other folk into public works such as the construction of a great wall, the greatest wall ever trust me and the only exemptions given out for this sort of conscription would have been for the members of the scholar-gentry elite. Military conscription was also similar in that able-bodied peasants or criminal convicts would be drafted into the military to help supplement the military's garrisoned strength.^(1) I couldn't find anything about an increase in organized conscription during the end of a dynasty, but I would personally find this unlikely as by the time a dynasty was due for replacement, there were usually systemic issues that prevented effective administration of the government and the people.
First, it should be noted that a "change in families" was not an ordinary occurrence- a change in ruling family meant the end of a dynasty and the founding of a new one, and this almost never happened except due to invasion, civil war, or a combination of both. Which is to say, these are emergency situations where standard procedure can go out the window and desperate measures may be taken. Some dynastic transitions happened fairly quickly (for example, the Qin-Western Han transition, or the Sui-Tang one) and caused relatively little disruption to ordinary life; some, like the collapse of the Eastern Han or of the Western Jin, could drag on for decades and lead to many people being displaced or killed by battle, famine or disease.
Second, exactly how conscription worked, and who was subject to it, varied greatly over time. So, for example, under the Western Han every healthy adult male could be conscripted. Ordinarily they would serve for a few years in either the frontier garrisons or the imperial guard at the capital then return home, but they could be called up again if a large army was being raised for a campaign. But in the Eastern Han, conscription was abolished for a time and armies were raised entirely from volunteers, convicts and foreign allies. In the time when the Song of Mulan first appears, during the Northern Wei period, conscription was not universal but certain households had a responsibility to furnish one well-armed soldier- in the original story, Mulan came from one of these military families and served in place of her aging father and her underage little brother.
Third, there are many instances of purges and massacres in the history of Chinese court politics, but this would generally only happen to rich and powerful families at high levels of government. A change in dynasty could be followed by a purge of powerful figures that the new rulers don't trust- but to bring this down to the level of ordinary farmers and townspeople wouldn't serve a purpose for them. So while conscription, sieges, looting armies, food shortages and plagues could all terrorize the common people during the wars surrounding a dynastic transition, once the fighting stopped the new rulers were generally interested in getting back to business as usual so that the peasants could generate taxes for them.
So, in summary, if you're an ordinary Chinese peasant during a dynastic change, your odds of being drafted may vary, but at any rate you probably don't need to worry about reprisals after the disturbance is over.
Conscription varied widely depending on the timeperiod and even varied widely within a single dynasty. As mentioned by others here, the Western Han era had universal conscription of a well trained milita where the levies would be trained for 1 year and served for another 1-2 years. During the Eastern Han era, conscription was deemphasized and could be avoided by paying a fee, and was mostly abolished for much of the Eastern Han era as the military favored volunteers (professionals, semi-professionals, mercenaries, and conscript volunteers). The Sui and Tang Dynasties adopted hereditary military recruitment and a national guard type system where designated soldiers would farm during peacetime but were mobilized during war, while the late Tang Dynasty moved to professional and mercenary armies.